1. Field of the Invention
The present invention relates to the field of semiconductor processing and, more particularly, to run-to-run control in semiconductor processing.
2. Description of the Related Art
Run-to-run (R2R) control and fault detection (FDC) in semiconductor processing refers to the practice of updating equipment recipe settings based upon product measurements that occur after process completion. The practice applies in the semiconductor industry due to the inability to measure the product characteristics in situ. For example, in the chemical-mechanical-planarization (CMP) process, pad rotational speeds, applied forces, and other parameters are measurable, but the film thickness, the actual product variable, is not. Similarly, in lithography, the exposure power, exposure time and focus may be determined, but the actual overlay errors are not measured until after the development of the resist, a separate process occurring long after the lithographic exposure. Other examples exist, but the primary applications occur in lithography (overlay and critical dimension (CD)), plasma etch and CMP.
The best way to implement effective R2R control is with an approach using a reliable process model due to the long measurement delays often associated with these implementations. However, a common problem in the R2R control and FDC of these processes is that the model coefficients are not well known and that the experiments to refine the values are too laborious. A need exists for an approach to simultaneously estimate the state of the process and refine the model coefficients using data gathered during closed-loop controller operation. Complicating this problem is the fact that some of the state variables and some of the model coefficients reflect information on different components of the problem. For example, some coefficients may be product dependent, but not tool dependent. Some of the state variables may reflect the state of some aspect of the tool and others may reflect the contribution of a consumable or auxiliary component, like a reticle. A method that accommodates these needs in effective R2R control would solve many manufacturing difficulties in making semiconductors.
In the prior art, a method for combined state and parameter estimation in a run-to-run control application has not been available. Various approaches to parts of the problem are known. In the prior art, state estimation is utilized to estimate the tool state from the measured data, assuming the product contributions are known, constant and included in the model. However, if the model contains some coefficient errors, an inevitable eventuality, then using the control system to control processes producing more than one product causes apparent disturbance changes each time the product changes. Product changes in a typical foundry fab occur essentially every lot of wafers. Thus, disturbance estimation with a constant model delivers performance that is highly dependent on the accuracy of the model coefficients.
In the prior art, others implement an adaptive form of the estimator that estimates a model coefficient that characterizes the current state of the tool, but ignores the additive disturbance contributed by the process tool or consumables in the process. This approach introduces the same problem as disturbance estimation alone. The controller attributes all of the error to the model coefficients. Since different products have different model coefficients, and the tool disturbance is commingled with product contribution in the coefficients, when products are switched in production, the errors propagate, appearing in the output as random errors. However the errors are not random, but instead are due to the inability of the system to properly assign the sources of errors.
What is needed is a method to combine the capability to do both additive state disturbance estimation and model parameter estimation so that the error sources are properly assigned, allowing product switching with minimum system upset. What is further needed is an approach to this problem that (i) combines parameter and state/parameter estimation using manufacturing data to simultaneously refine the product and auxiliary model contributions; and (ii) estimates the tool state.
Having a reliable process model is essential to implementing an effective run-to-run (R2R) control system, particularly in view of the long measurement delays associated with such systems. A need has existed for an approach that both estimates the state of the process and refines the model coefficients using data gathered during closed-loop controller operation.
In accordance with the present invention, a method for combined state and parameter estimation in a R2R control application is provided. More particularly, the method for controlling a manufacturing process includes: processing materials using a process input and producing a process output, storing the process input in a database, the storing including using a timestamp, and storing at least one measurement of the process output in the database aligned with each process input using the timestamp. The method further includes iterating over the data in the database to estimate one or more coefficients for a model, and, if one or more measurements is missing, replacing the missing measurements based on a prediction from said model. The model is updated with said coefficient estimates. The method additionally includes iterating over the data from the database to estimate a process state, and, if one or more of the measurements is missing from the database, replacing the missing measurements for the database based on prediction from the model. The model is updated with said process state estimate. The replacement of missing measurements during parameter or state estimation can be accomplished implicitly or explicitly. A controller may receive the updated model and utilize the model to produce the next process input. The updated model may also be utilized to generate an estimate for a measurable process variable, wherein the estimate can be compared to an actual measurement to determine if the estimate is within confidence limits. If the estimate is not within confidence limits, a fault is indicated.
According to one embodiment, the method includes one or more modules coupled to the database, the one or more modules including at least a sorting module configured to sort measurements received asynchronously from the process according to the timestamp, the sorted measurements including later arriving measurements to allow the next process input to be based at least in part on an error calculated using later available measurements. The sorting module also sorts the data in the database for use during parameter estimation or state estimation.
If actual measurements become available a time period after model coefficient estimation or process state estimation, for one or more measurements which was missing, the predicted measurements for the previously missing measurements are replaced with the actual measurements, and the actual measurements are stored in the database. In subsequent model coefficient estimation and process state estimation, the actual measurements are used in place of the predicted measurements. The time period during which one is waiting for the actual measurements to become available may be variable in the present invention.
In one embodiment, the state estimator filter and parameter estimator filter comprise separate receding-horizon filters that compute estimates using a constrained least-squares approach. The least-squares optimization requires the solution to a quadratic program.